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Experimental measurements in plane Couette-Poiseuille flow: dynamics of the large- and small-scale flow. (English) Zbl 07315236
Summary: In this paper we experimentally study the transitional range of Reynolds numbers in plane Couette-Poiseuille flow, focusing our attention on the localized turbulent structures triggered by a strong impulsive jet and the large-scale flow generated around these structures. We present a detailed investigation of the large-scale flow and show how its amplitude depends on Reynolds number and amplitude perturbation. In addition, we characterize the initial dynamics of the localized turbulent spot, which includes the coupling between the small and large scales, as well as the dependence of the advection speed on the large-scale flow generated around the spot. Finally, we provide the first experimental measurements of the large-scale flow around an oblique turbulent band.

76 Fluid mechanics
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[1] Amini, J. & Lespinard, G.1982Experimental study of an ‘incipient spot’ in a transitional boundary layer. Phys. Fluids25 (10), 1743-1750.
[2] Andereck, C.D., Liu, S.S. & Swinney, H.L.1986Flow regimes in a circular Couette system with independently rotating cylinders. J.Fluid Mech.164, 155-183.
[3] Avila, K., Moxey, D., De Lozar, A., Avila, M., Barkley, D. & Hof, B.2011The onset of turbulence in pipe flow. Science333 (6039), 192-196.
[4] Avila, M., Willis, A.P. & Hof, B.2010On the transient nature of localized pipe flow turbulence. J.Fluid Mech.646, 127-136. · Zbl 1189.76262
[5] Bakchinov, A.A., Westin, K.J.A., Kozlov, V.V. & Alfredsson, P.H.1998Experiments on localized disturbances in a flat plate boundary layer. Part 2. Interaction between localized disturbances and TS-waves. Eur. J. Mech. B/Fluids17 (6), 847-873. · Zbl 0925.76005
[6] Barkley, D.2016Theoretical perspective on the route to turbulence in a pipe. J.Fluid Mech.803, P1. · Zbl 1454.76047
[7] Barkley, D. & Tuckerman, L.S.2005Computational study of turbulent laminar patterns in Couette flow. Phys. Rev. Lett.94 (1), 014502-4.
[8] Barkley, D. & Tuckerman, L.S.2007Mean flow of turbulent-laminar patterns in plane Couette flow. J.Fluid Mech.576, 109-137. · Zbl 1124.76018
[9] Brand, E. & Gibson, J.F.2014A doubly localized equilibrium solution of plane Couette flow. J.Fluid Mech.750, R3.
[10] Brethouwer, G., Duguet, Y. & Schlatter, P.2012Turbulent-laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces. J.Fluid Mech.704, 137-172. · Zbl 1246.76028
[11] Breuer, K.S. & Haritonidis, J.H.1990The evolution of a localized disturbance in a laminar boundary layer. Part 1. Weak disturbances. J.Fluid Mech.220, 569-594.
[12] Breuer, K.S. & Landahl, M.T.1990The evolution of a localized disturbance in a laminar boundary layer. Part 2. Strong disturbances. J.Fluid Mech.220, 595-621.
[13] Chantry, M., Tuckerman, L.S. & Barkley, D.2016Turbulent-laminar patterns in shear flows without walls. J.Fluid Mech.791, R8. · Zbl 1382.76106
[14] Chantry, M., Tuckerman, L.S. & Barkley, D.2017Universal continuous transition to turbulence in a planar shear flow. J.Fluid Mech.824, R1.
[15] Chen, P.2004Measurement of mean flows of Faraday waves. Phys. Rev. Lett.93 (6), 064504-4.
[16] Cherubini, S., De Palma, P., Robinet, J.-C. & Bottaro, A.2011The minimal seed of turbulent transition in the boundary layer. J.Fluid Mech.689, 221-253. · Zbl 1241.76246
[17] Cherubini, S., Robinet, J.-C., Bottaro, A. & De Palma, P.2010Optimal wave packets in a boundary layer and initial phases of a turbulent spot. J.Fluid Mech.656, 231-259. · Zbl 1197.76045
[18] Coles, D.1965Transition in circular Couette flow. J.Fluid Mech.21 (03), 385-425. · Zbl 0134.21705
[19] Coles, D. & Van Atta, C.1966Progress report on a digital experiment in spiral turbulence. AIAA J.4 (11), 1969-1971.
[20] Couliou, M. & Monchaux, R.2015Large-scale flows in transitional plane Couette flow: a key ingredient of the spot growth mechanism. Phys. Fluids27 (3), 034101. · Zbl 1383.76188
[21] Couliou, M. & Monchaux, R.2017Growth dynamics of turbulent spots in plane Couette flow. J.Fluid Mech.819, 1-20. · Zbl 1383.76188
[22] Couliou, M. & Monchaux, R.2018Childhood of turbulent spots in a shear flow. Phys. Rev. Fluids3 (12), 123901-12.
[23] Croquette, V, Le Gal, P., Pocheau, A & Guglielmetti, R1986Large-scale flow characterization in a Rayleigh-Bénard convective pattern. Eur. Phys. Lett.1 (8), 393-399.
[24] Croquette, V. & Pocheau, A.1984 Wavenumber selection in Rayleigh-Bénard convective structure. In Cellular Structures in Instabilities (ed. J.E. Wesfreid & S. Zaleski), pp. 104-126. Springer.
[25] Cross, M.C. & Hohenberg, P.C.1993Pattern formation outside of equilibrium. Rev. Mod. Phys.65 (3), 851-1112. · Zbl 1371.37001
[26] Darbyshire, A.G. & Mullin, T.1995Transition to turbulence in constant-mass-flux pipe flow. J.Fluid Mech.289, 83-114.
[27] Daviaud, F., Hegseth, J. & Bergé, P.1992Subcritical transition to turbulence in plane Couette flow. Phys. Rev. Lett.69 (17), 2511-2514.
[28] Dessup, T., Tuckerman, L.S., Wesfreid, J.E., Barkley, D. & Willis, A.P.2018Self-sustaining process in Taylor-Couette flow. Phys. Rev. Fluids3 (12), 123902-10.
[29] Deusebio, E., Brethouwer, G., Schlatter, P. & Lindborg, E.2014A numerical study of the unstratified and stratified Ekman layer. J.Fluid Mech.755, 672-704.
[30] Duguet, Y. & Schlatter, P.2013Oblique laminar-turbulent interfaces in plane shear flows. Phys. Rev. Lett.110 (3), 034502-4.
[31] Duguet, Y., Schlatter, P. & Henningson, D.S.2010Formation of turbulent patterns near the onset of transition in plane Couette flow. J.Fluid Mech.650, 119-129. · Zbl 1189.76254
[32] Duriez, T., Aider, J.-L. & Wesfreid, J.E.2009Self-sustaining process through streak generation in a flat-plate boundary layer. Phys. Rev. Lett.103 (14), 144502-4.
[33] Eckhardt, B.2018Transition to turbulence in shear flows. Physica A504, 121-129.
[34] Fukudome, K. & Iida, O.2012Large-scale flow structure in turbulent Poiseuille flows at low-Reynolds numbers. JFST7 (1), 181-195.
[35] Fukudome, K., Iida, O. & Nagano, Y.2010Large-scale structure and the sustenance mechanism in turbulent Poiseuille flow at low Reynolds number. Trans. Jpn Soc. Mech. Engng B76 (771), 1773-1778.
[36] Gad-El-Hak, M., Blackwelderf, R.F. & Riley, J.J.1981On the growth of turbulent regions in laminar boundary layers. J.Fluid Mech.110, 73-95.
[37] Gomé, S., Tuckerman, L.S. & Barkley, D.2020Statistical transition to turbulence in plane channel flow. Phys. Rev. Fluids5 (8), 083905-20.
[38] Greenside, H.S., Cross, M.C. & Coughran, W.M.1988Mean flows and the onset of chaos in large-cell convection. Phys. Rev. Lett.60 (22), 2269-2272.
[39] Hashimoto, S., Hasobe, A., Tsukahara, T., Kawaguchi, Y. & Kawamura, H.2009 An experimental study on turbulent-stripe structure in transitional channel flow. In Proc. 6th Int. Symp. on Turbulence, Heat and Mass Transfer, pp. 193-196.
[40] Hayot, F. & Pomeau, Y.1994Turbulent domain stabilization in annular flows. Phys. Rev. E50 (3), 2019-2021.
[41] Hegseth, J.J., Andereck, C.D., Hayot, F. & Pomeau, Y.1989Spiral turbulence and phase dynamics. Phys. Rev. Lett.62 (3), 257-260.
[42] Henningson, D.S.1989Wave growth and spreading of a turbulent spot in plane Poiseuille flow. Phys. Fluids1 (11), 1876-1882. · Zbl 0684.76056
[43] Henningson, D.S. & Alfredsson, P.H.1987The wave structure of turbulent spots in plane Poiseuille flow. J.Fluid Mech.178, 405-421.
[44] Henningson, D.S. & Kim, J.1991On turbulent spots in plane Poiseuille flow. J.Fluid Mech.228, 183-205. · Zbl 0723.76048
[45] Hof, B., De Lozar, A., Kuik, D.J. & Westerweel, J.2008Repeller or attractor? Selecting the dynamical model for the onset of turbulence in pipe flow. Phys. Rev. Lett.101 (21), 214501-4.
[46] Horii, S., Sagawa, Y., Miyazaki, M. & Matsubara, M.2017 Very large-scale feature of transitional and turbulent channel flows: dependence on facilities. In Progress in Turbulence VII (ed. R. Örlü, A. Talamelli, M. Oberlack & J. Peinke), pp. 189-195. Springer International Publishing.
[47] Huey, L.J. & Williamson, J.W.1974Plane turbulent Couette flow with zero net flow. J.Appl. Mech.41 (4), 885-890.
[48] Ishida, T., Brethouwer, G., Duguet, Y. & Tsukahara, T.2017aLaminar-turbulent patterns with rough walls. Phys. Rev. Fluids2 (7), 073901-24.
[49] Ishida, T., Duguet, Y. & Tsukahara, T.2016Transitional structures in annular Poiseuille flow depending on radius ratio. J.Fluid Mech.794, R2.
[50] Ishida, T., Duguet, Y. & Tsukahara, T.2017bTurbulent bifurcations in intermittent shear flows: from puffs to oblique stripes. Phys. Rev. Fluids2 (7), 073902-18.
[51] Kashyap, P.V., Duguet, Y. & Chantry, M.2020Far field of turbulent spots. Phys. Rev. Fluids5 (10), 103902-18.
[52] Khapko, T., Schlatter, P., Duguet, Y. & Henningson, D.S.2016Turbulence collapse in a suction boundary layer. J.Fluid Mech.795, 356-379. · Zbl 1359.76144
[53] Klingmann, B.G.B.1992On transition due to three-dimensional disturbances in plane Poiseuille flow. J.Fluid Mech.240, 167-195.
[54] Klingmann, B.G.B. & Alfredsson, P.H.1991 Experiments on the evolution of a point-like disturbance in plane Poiseuille flow into a turbulent spot. In Advances in Turbulence, vol. 3, pp. 182-188. Springer.
[55] Klotz, L., Gumowski, K. & Wesfreid, J.E.2019Experiments on a jet in a crossflow in the low-velocity-ratio regime. J.Fluid Mech.863, 386-406.
[56] Klotz, L., Lemoult, G., Frontczak, I., Tuckerman, L.S. & Wesfreid, J.E.2017Couette-Poiseuille flow experiment with zero mean advection velocity: subcritical transition to turbulence. Phys. Rev. Fluids2 (4), 043904-19.
[57] Klotz, L. & Wesfreid, J.E.2017Experiments on transient growth of turbulent spots. J.Fluid Mech.829, R4. · Zbl 07136098
[58] Kuik, D.J., Poelma, C. & Westerweel, J.2010Quantitative measurement of the lifetime of localized turbulence in pipe flow. J.Fluid Mech.645, 529-539. · Zbl 1189.76031
[59] Lagha, M. & Manneville, P.2007Modeling of plane Couette flow. I. Large scale flow around turbulent spots. Phys. Fluids19 (9), 094105. · Zbl 1182.76422
[60] Lemoult, G., Aider, J.L. & Wesfreid, J.E.2013Turbulent spots in a channel: large-scale flow and self-sustainability. J.Fluid Mech.731, R1. · Zbl 1294.76165
[61] Lemoult, G., Gumowski, K., Aider, J.-L. & Wesfreid, J.E.2014Turbulent spots in channel flow: an experimental study: large-scale flow, inner structure and low-order model. Eur. Phys. J. E37 (4), 25.
[62] Lemoult, G., Shi, L., Avila, K., Jalikop, S.V., Avila, M. & Hof, B.2016Directed percolation phase transition to sustained turbulence in Couette flow. Nat. Phys.12, 254-258.
[63] Liu, T., Semin, B., Klotz, L., Godoy-Diana, R., Wesfreid, J.E. & Mullin, T.2021 Decay of streaks and rolls in plane Couette-Poiseuille flow. arXiv:2008.08851.
[64] Lu, J., Tao, J., Zhou, W. & Xiong, X.2019Threshold and decay properties of transient isolated turbulent band in plane Couette flow. Appl. Math. Mech.-Engl. Ed.40, 1449-1456.
[65] Lundbladh, A. & Johansson, A.V.1991Direct simulation of turbulent spots in plane Couette flow. J.Fluid Mech.229, 499-516. · Zbl 0850.76256
[66] Manneville, P.2009Spatiotemporal perspective on the decay of turbulence in wall-bounded flows. Phys. Rev. E79 (2), 025301-4.
[67] Manneville, P.2016Turbulent patterns made simple?J.Fluid Mech.796, 1-4.
[68] Manneville, P.2017Laminar-turbulent patterning in transitional flows. Entropy19 (7), 316.
[69] Manneville, P.2018On the generation of drift flows in wall-bounded flows transiting to turbulence. TAML8 (1), 48-56.
[70] Mautner, T.S. & Van Atta, C.W.1982An experimental study of the wall-pressure field associated with a turbulent spot in a laminar boundary layer. J.Fluid Mech.118, 59-77.
[71] Mukund, V. & Hof, B.2018The critical point of the transition to turbulence in pipe flow. J.Fluid Mech.839, 76-94. · Zbl 1419.76270
[72] Mutabazi, I., Hegseth, J.J., Andereck, C.D. & Wesfreid, J.E.1990Spatiotemporal pattern modulations in the Taylor-Dean system. Phys. Rev. Lett.64 (15), 1729-1732.
[73] Newell, A.C., Passot, T. & Lega, J.1993Order parameter equations for patterns. Annu. Rev. Fluid Mech.25 (1), 399-453.
[74] Peixinho, J. & Mullin, T.2007Finite-amplitude thresholds for transition in pipe flow. J.Fluid Mech.582, 169-178. · Zbl 1114.76304
[75] Philip, J. & Manneville, P.2011From temporal to spatiotemporal dynamics in transitional plane Couette flow. Phys. Rev. E83 (3), 036308-12.
[76] Pocheau, A. & Daviaud, F.1997Sensitivity of convective structures to mean flow boundary conditions: acorrelation between symmetry and dynamics. Phys. Rev. E55 (1), 353-373.
[77] Pomeau, Y.1986Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D23 (1-3), 3-11.
[78] Pomeau, Y.2015The transition to turbulence in parallel flows: a personal view. C. R. Méc343 (3), 210-218.
[79] Prigent, A., Grégoire, G., Chaté, H. & Dauchot, O.2003Long-wavelength modulation of turbulent shear flows. Physica D174 (1-4), 100-113. · Zbl 1036.76023
[80] Prigent, A., Grégoire, G., Chaté, H., Dauchot, O. & Van Saarloos, W.2002Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett.89 (1), 014501-4.
[81] Reetz, F., Kreilos, T. & Schneider, T.M.2019Exact invariant solution reveals the origin of self-organized oblique turbulent-laminar stripes. Nat. Commun.10, 2277.
[82] Riley, J.J. & Gad-El-Hak, M.1985 The dynamics of turbulent spots. In Frontiers in Fluid Mechanics, pp.123-155. Springer.
[83] Rolland, J.2014Turbulent spot growth in plane Couette flow: statistical study and formation of spanwise vorticity. Fluid Dyn. Res.46 (1), 015512. · Zbl 1433.76056
[84] Schmid, P.J. & Henningson, D.S.2001Stability and Transition in Shear Flows. Springer.
[85] Schumacher, J. & Eckhardt, B.2001Evolution of turbulent spots in a parallel shear flow. Phys. Rev. E63 (4), 046307-9.
[86] Seki, D. & Matsubara, M.2012Experimental investigation of relaminarizing and transitional channel flows. Phys. Fluids24 (12), 124102.
[87] Shih, H.-Y., Hsieh, T.-L. & Goldenfeld, N.2016Ecological collapse and the emergence of travelling waves at the onset of shear turbulence. Nat. Phys.12, 245-248.
[88] Shimizu, M. & Manneville, P.2019Bifurcations to turbulence in transitional channel flow. Phys. Rev. Fluids4 (11), 113903-21.
[89] Siggia, E.D. & Zippelius, A.1981aDynamics of defects in Rayleigh-Bénard convection. Phys. Rev. A24 (2), 1036-1049.
[90] Siggia, E.D. & Zippelius, A.1981bPattern selection in Rayleigh-Bénard convection near threshold. Phys. Rev. Lett.47 (12), 835-838.
[91] Tao, J.J., Eckhardt, B. & Xiong, X.M.2018Extended localized structures and the onset of turbulence in channel flow. Phys. Rev. Fluids3 (1), 011902-7.
[92] Tillmark, N.1995On the spreading mechanisms of a turbulent spot in plane Couette flow. Eur. Phys. Lett.32 (6), 481-485.
[93] Tillmark, N. & Alfredsson, P.H.1992Experiments on transition in plane Couette flow. J.Fluid Mech.235, 89-102.
[94] Tsanis, I.K. & Leutheusser, H.J.1988The structure of turbulent shear-induced countercurrent flow. J.Fluid Mech.189, 531-552.
[95] Tsukahara, T., Seki, Y., Kawamura, H. & Tochio, D.2005 DNS of turbulent channel flow at very low Reynolds numbers. In Proc. 4th Int. Symp. on Turbulence and Shear Flow Phenomena, pp. 935-940.
[96] Tsukahara, T., Tillmark, N. & Alfredsson, P.H.2010Flow regimes in a plane Couette flow with system rotation. J.Fluid Mech.648, 5-33. · Zbl 1189.76047
[97] Tuckerman, L.S. & Barkley, D.2011Patterns and dynamics in transitional plane Couette flow. Phys. Fluids23 (4), 041301. · Zbl 1308.76135
[98] Tuckerman, L.S., Chantry, M. & Barkley, D.2020Patterns in wall-bounded shear flows. Annu. Rev. Fluid Mech.52 (1), 343-367. · Zbl 1439.76032
[99] Tuckerman, L.S., Kreilos, T., Schrobsdorff, H., Schneider, T.M. & Gibson, J.F.2014Turbulent-laminar patterns in plane Poiseuille flow. Phys. Fluids26 (11), 114103.
[100] Waleffe, F.1997On a self-sustaining process in shear flows. Phys. Fluids9 (4), 883-900.
[101] Wang, Z., Guet, C., Monchaux, R., Duguet, Y. & Eckhardt, B.2020Quadrupolar flows around spots in internal shear flows. J.Fluid Mech.892, A27. · Zbl 07190261
[102] Westin, K.J.A., Bakchinov, A.A., Kozlov, V.V. & Alfredsson, P.H.1998Experiments on localized disturbances in a flat plate boundary layer. Part 1. The receptivity and evolution of a localized free stream disturbance. Eur. J. Mech. B/Fluids17 (6), 823-846. · Zbl 0925.76005
[103] Xiao, X. & Song, B.2020The growth mechanism of turbulent bands in channel flow at low Reynolds numbers. J.Fluid Mech.883, R1. · Zbl 1430.76322
[104] Xiong, X., Tao, J., Chen, S. & Brandt, L.2015Turbulent bands in plane-Poiseuille flow at moderate Reynolds numbers. Phys. Fluids27 (4), 041702.
[105] Zammert, S. & Eckhardt, B.2014Streamwise and doubly-localised periodic orbits in plane Poiseuille flow. J.Fluid Mech.761, 348-359.
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